Layered periodic foundations (LPFs) with identical unit cells have been proposed as a type of seismic metamaterials due to the unique dynamic characteristic of attenuation zones. Additionally, experimental studies on a single storey frame and numerical studies on a ten storey frame conducted with chosen configurations of periodic foundations showed that both 1D two-layer and 1D three-layer periodic foundations are effective in attenuating the vibration responses of structural systems. The effect of material and geometric parameters on the first attenuation zone of 1D three-layer foundation has also been investigated in the present study. The results obtained from the analysis have shown wider attenuation zones with lower starting frequencies in the 1D three-layer periodic foundation as compared to a 1D two-layer periodic foundation. The generalized formulation has then been applied to the case of a 1D periodic foundation with three material layers. In the present study the PWE method has been formulated to analyse a generic multi-layer periodic unit cell.
#Dispersio. doece periodic tavl series
The band gap characteristics of 1D periodic foundations can be computed through the Plane Wave Expansion (PWE) method by expressing material properties in the form of Fourier series expansion in the reciprocal lattice space and obtaining the band gap through an eigenvalue problem using Bloch’s theorem. Periodic foundations can be one dimensional (1D) or two dimensional (2D) or three dimensional (3D) periodic foundations depending of the arrangement of the periodic materials in the foundation. This frequency range is called the band gap or the attenuation zone of the periodic structure. Periodic structures have the ability to block the passage of elastic waves within a certain frequency range through them. Concepts from solid state physics have led to the evolution of a new technique of base isolation for civil engineering structures through the use of a foundation system consisting of periodic materials, namely periodic foundation.
Conventional base isolators like lead rubber bearing, high damping rubber bearing and friction pendulum bearing are not suitable for structures containing crucial pipelines and other sensitive structural components, since these structures with conventional isolators are usually subjected to large relative displacements between the superstructure and the base.
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